Problem: Simplify the following expression: $ n = \dfrac{-y}{-9y - 9} + \dfrac{1}{8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-y}{-9y - 9} \times \dfrac{8}{8} = \dfrac{-8y}{-72y - 72} $ Multiply the second expression by $\dfrac{-9y - 9}{-9y - 9}$ $ \dfrac{1}{8} \times \dfrac{-9y - 9}{-9y - 9} = \dfrac{-9y - 9}{-72y - 72} $ Therefore $ n = \dfrac{-8y}{-72y - 72} + \dfrac{-9y - 9}{-72y - 72} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-8y - 9y - 9}{-72y - 72} $ $n = \dfrac{-17y - 9}{-72y - 72}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{17y + 9}{72y + 72}$